Details

sample117.0ms

Algorithm

intervals

Results

27.0ms	63×	body	1280	valid
25.0ms	42×	body	320	valid
21.0ms	326×	body	80	valid
15.0ms	54×	body	640	valid
3.0ms	20×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	15	7
2	32	7
3	69	7
4	146	7
5	296	7
6	884	7
7	4473	7
done	5000	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize13.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (sin x) (sinh y))
12.1b	(/ (* (sin x) (sinh y)) x)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow1`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `expm1-log1p-u` `sinh-def` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l/` `associate-/l` `unswap-sqr`

Counts

2 → 45

Calls

2 calls:

24.0ms	(* (sin x) (sinh y))
18.0ms	(/ (* (sin x) (sinh y)) x)

series276.0ms

Counts

2 → 6

Calls

2 calls:

140.0ms	(* (sin x) (sinh y))
136.0ms	(/ (* (sin x) (sinh y)) x)

simplify859.0ms

Counts

51 → 51

Iterations

Useful iterations: done (857.0ms)

Iter	Nodes	Cost
0	112	500
1	279	477
2	1524	417
done	5000	416

prune188.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (sinh y) x)
0.4b	(* (sin x) (/ (sinh y) x))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`times-frac`
18×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
9×	`add-exp-log` `add-cbrt-cube`
4×	`pow1`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
1×	`sinh-def` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `associate-/l/`

Counts

2 → 64

Calls

2 calls:

16.0ms	(/ (sinh y) x)
27.0ms	(* (sin x) (/ (sinh y) x))

series227.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(/ (sinh y) x)
143.0ms	(* (sin x) (/ (sinh y) x))

simplify998.0ms

Counts

70 → 70

Iterations

Useful iterations: done (996.0ms)

Iter	Nodes	Cost
0	136	698
1	340	662
2	1656	593
done	5000	590

prune235.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/6 (/ (pow y 3) x) (/ y x))
0.2b	(* (sin x) (fma (/ (pow y 5) x) 1/120 (fma 1/6 (/ (pow y 3) x) (/ y x))))
1.1b	(/ (pow y 5) x)
4.7b	(/ (pow y 3) x)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

57×	`times-frac`
49×	`add-sqr-sqrt`
47×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
19×	`associate-/l*`
16×	`add-exp-log`
12×	`cube-prod`
10×	`add-cbrt-cube`
8×	`sqr-pow`
6×	`pow1` `div-exp` `associate-/r*`
4×	`expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `fma-udef`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 146

Calls

4 calls:

0.0ms	(fma 1/6 (/ (pow y 3) x) (/ y x))
13.0ms	(* (sin x) (fma (/ (pow y 5) x) 1/120 (fma 1/6 (/ (pow y 3) x) (/ y x))))
22.0ms	(/ (pow y 5) x)
15.0ms	(/ (pow y 3) x)

series346.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(fma 1/6 (/ (pow y 3) x) (/ y x))
232.0ms	(* (sin x) (fma (/ (pow y 5) x) 1/120 (fma 1/6 (/ (pow y 3) x) (/ y x))))
41.0ms	(/ (pow y 5) x)
28.0ms	(/ (pow y 3) x)

simplify1.1s

Counts

158 → 158

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	236	2061
1	479	1875
2	2134	1742
done	5002	1739

prune655.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize54.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt y)
2.0b	(/ (pow (* (cbrt y) (cbrt y)) 5) (* (cbrt x) (cbrt x)))
2.4b	(/ (pow (cbrt y) 5) (cbrt x))
4.7b	(/ (pow y 3) x)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

101×	`times-frac`
75×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
57×	`cbrt-prod`
56×	`unpow-prod-down`
34×	`add-exp-log`
27×	`associate-/l*`
14×	`div-exp`
13×	`sqr-pow`
12×	`cube-prod`
10×	`associate-/r*` `add-cbrt-cube`
6×	`pow-exp` `prod-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `cube-mult` `pow-to-exp` `unpow3` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `div-inv`
1×	`pow1/3` `cbrt-unprod`

Counts

4 → 205

Calls

4 calls:

1.0ms	(cbrt y)
20.0ms	(/ (pow (* (cbrt y) (cbrt y)) 5) (* (cbrt x) (cbrt x)))
15.0ms	(/ (pow (cbrt y) 5) (cbrt x))
15.0ms	(/ (pow y 3) x)

series628.0ms

Counts

4 → 12

Calls

4 calls:

260.0ms	(cbrt y)
190.0ms	(/ (pow (* (cbrt y) (cbrt y)) 5) (* (cbrt x) (cbrt x)))
137.0ms	(/ (pow (cbrt y) 5) (cbrt x))
42.0ms	(/ (pow y 3) x)

simplify1.2s

Counts

217 → 217

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	337	2890
1	656	2598
2	2393	2404
done	5000	2375

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

regimes232.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	56
1	32	56
done	32	56

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.2s	10328×	body	80	valid
1.1s	1978×	body	640	valid
836.0ms	1851×	body	1280	valid
276.0ms	1095×	body	320	valid
90.0ms	649×	body	160	valid